Figure 4

Decreasing inter-publication waiting time$\mathit{\tau }\mathbf{(}\mathit{n}\mathbf{)}$is quantitative evidence for cumulative advantage in science. (A) Schematic of a science career, where major accomplishments sustain career growth. Specifically, publications in high-impact journals serve as a record of scientists capitalizing on opportunities for success, and the duration ${\tau }_i^j(n)$ between a scientist’s success n and success $n+1$ provide a quantitative method for analyzing cumulative advantage. We search for quantitative evidence of self-reinforcing social mechanisms by analyzing productivity patterns in specific journal sets that are highly competitive and widely targeted. (B) The average waiting time $〈{\tau }^j(n)〉$ between publication n and publication $n+1$ shows a significant decreasing trend as an author continues to publish in a given journal set. A decreasing ${\tau }^j(n)$ between publications suggests that an advanced publication career (larger n) facilitates future publications by leveraging reputation, expertise, seniority, and other cumulative resources. The values of $〈{\tau }^j(1)〉$ are 2.9 yrs. (Cell), 2.4 yrs. (Econ.), 2.8 yrs. (Mgmt. Sci.), 3.6 yrs. (Nat./PNAS/Sci.), 4.3 yrs. (NEJM) and 3.1 yrs. (PRL). The journal PRL exhibits a more rapid decline in $\tau (n)$ because of possible rapidity in successive publications (often by large high-energy experiment collaborations that publish many publications together in a single issue). Only research profiles with $L\ge 5$ years and $N_p\ge 5$ are included in the calculation of these inter-event waiting-time curves. In order to reduce censoring bias arising form careers that started before the beginning of each data sample, we only included trajectories with the first publication year $y_{i,0}^j\ge 1970$ for the natural and management sciences and $y_{i,0}^j\ge 1960$ for the economic sciences. (C, D) Complementary cumulative probability distribution, $P(\ge \tau (n))$, for publications $n=1,\dots ,15$ in (C) the Economics and (D) Nat./PNAS/Sci. journal sets. The distributions are right-skewed, indicating the possibility of a relatively long waiting time $\tau (n)$ for all n. However, by $n=10$ the observed likelihood of waiting 3 or more years, $P(\ge 3|n=10)$, falls to roughly 0.2 for both Econ. and Nat./PNAS/Sci.